NetworkX：如何创建加权图的关联矩阵？ [英] NetworkX: how to create an incidence matrix of a weighted graph?

问题描述

创建了一个像这样的网格网络： $ _

  from __future__ import division 
 import networkx as nx 
 from pylab import * 
 import matplotlib.pyplot as plt 
％pylab inline 
 
 ncols = 10 
 
 N = 10＃每边节点$ b （）（）（）中的i，j）（b（g，n，grid_2d_graph，N，N） 
 nx.relabel_nodes（G，labels，False）
 inds = labels.keys（）
 vals = labels.values（）
 inds = [（Nj-1，Ni- 1）for i，j in inds] 
 pos2 = dict（zip（vals，inds））
  

  
每个边缘都有一个与其长度相对应的权重（在这个微不足道的例子中，所有长度都等于1） ＃权重
从数学导入sqrt 
 
权重= dict（）
在源代码中，目标在G.edges（）中：
 x1，y1 = pos2 [source] 
 x2，y2 = pos2 [target] 
 weights [（source，target）] = round（（math.sqrt（（x2-x1）** 2 +（y2-y1）** 2） ），3）
 
 for e在G.edges（）中：
 G [e [0]] [e [1]] =权重s [e]＃将权重分配给G.edges（）
  

这就是我的 G.edges（）看起来像：（startnode ID，endnode ID，weight）

  [（0,1,1.0），
（0,10,1.0），
（1,11,1.0），
（1,2,1.0），...]平凡的情况：所有权重都是单一的
  

如何创建考虑权重的关联矩阵刚刚被定义？我想使用 nx.incidence_matrix（G，nodelist = None，edgelist = None，oriented = False，weight = None），但是正确的值为权重在这种情况下？ docs 表示 weight 是表示用于提供矩阵中每个值的边缘数据关键字的字符串，但它是什么意思特别？我也没有找到相关的例子。

有什么想法吗？

解决方案

下面是一个简单的例子，展示了如何正确设置边缘属性以及如何生成加权关联矩阵。

  import networkx as nx 
从数学导入sqrt 
 
 G = nx.grid_2d_graph（3,3）
 for s，t in G.edges（）：
 x1，y1 = s 
 x2，y2 = t 
 G [s] [t] ['weight'] = sqrt（（x2-x1）** 2 +（y2-y1）** 2）* 42 
 
 print（nx.incidence_matrix（G，weight ='weight'）。todense（））
  

OUTPUT

  [[42. 42. 42. 0.0.0.0。 0。0。0] b $ b [0。0。42。42。42。0。0。0。0。0。0] 
 [42.0。0。 $ 0.42,0.0,0.0] 
 [0.0.0.0.0.0.42.42.42.0] 
 [0.42.4.2,0.0,0.42.4.22.4] 
 [0.0.0.0.0。 0.42 0. 0. 0. 42] 
 [0.0 0. 0. 0. 0. 0. 0. 42. 0. 0.] 
 [0。 0. 0. 0. 0. 42. 0. 0. 0. 42. 42.] 
 [0.0.42 0.42.0.0.0.0.0。 0.]] 
  

如果您想要矩阵中的节点和边的特定排序，请使用nodelist =和edgelist = networkx.indicence_matrix（）的可选参数。

Having created a grid network like this:

from __future__ import division
import networkx as nx
from pylab import *
import matplotlib.pyplot as plt
%pylab inline

ncols=10 

N=10 #Nodes per side
G=nx.grid_2d_graph(N,N)
labels = dict( ((i,j), i + (N-1-j) * N ) for i, j in G.nodes() )
nx.relabel_nodes(G,labels,False)
inds=labels.keys()
vals=labels.values()
inds=[(N-j-1,N-i-1) for i,j in inds]
pos2=dict(zip(vals,inds))

And having assigned each edge a weight corresponding to its length (in this trivial case, all lenghts=1):

#Weights
from math import sqrt

weights = dict()
for source, target in G.edges():
    x1, y1 = pos2[source]
    x2, y2 = pos2[target]
    weights[(source, target)] = round((math.sqrt((x2-x1)**2 + (y2-y1)**2)),3)

for e in G.edges():
    G[e[0]][e[1]] = weights[e] #Assigning weights to G.edges()

This is what my G.edges() looks like: (startnode ID, endnode ID, weight)

[(0, 1, 1.0),
 (0, 10, 1.0),
 (1, 11, 1.0),
 (1, 2, 1.0),... ] #Trivial case: all weights are unitary

How can I create an incidence matrix that takes into account the weights that have just been defined? I want to use nx.incidence_matrix(G, nodelist=None, edgelist=None, oriented=False, weight=None), but what is the correct value for weight in this case?

The docs say that weight is a string representing "the edge data key used to provide each value in the matrix", but what does it mean specifically? I have also failed to find relevant examples.

Any ideas?

解决方案

Here is a simple example showing how to properly set edge attributes and how to generate a weighted incidence matrix.

import networkx as nx
from math import sqrt

G = nx.grid_2d_graph(3,3)
for s, t in G.edges():
    x1, y1 = s
    x2, y2 = t
    G[s][t]['weight']=sqrt((x2-x1)**2 + (y2-y1)**2)*42

print(nx.incidence_matrix(G,weight='weight').todense())

OUTPUT

[[ 42.  42.  42.   0.   0.   0.   0.   0.   0.   0.   0.   0.]
 [  0.   0.   0.  42.  42.  42.   0.   0.   0.   0.   0.   0.]
 [ 42.   0.   0.   0.   0.   0.  42.   0.   0.   0.   0.   0.]
 [  0.   0.   0.   0.   0.   0.   0.  42.  42.  42.   0.   0.]
 [  0.  42.   0.  42.   0.   0.   0.   0.  42.   0.  42.   0.]
 [  0.   0.   0.   0.   0.   0.   0.  42.   0.   0.   0.  42.]
 [  0.   0.   0.   0.   0.  42.   0.   0.   0.  42.   0.   0.]
 [  0.   0.   0.   0.   0.   0.  42.   0.   0.   0.  42.  42.]
 [  0.   0.  42.   0.  42.   0.   0.   0.   0.   0.   0.   0.]]

If you want a particular ordering of the nodes and edges in the matrix use the nodelist= and edgelist= optional parameters to networkx.indicence_matrix().

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